Problem: Simplify the following expression: ${3(7+k)-5(3k-6)}$
Solution: Distribute the ${3}$ into the first set of parentheses: $ {3(}\gray{7+k}{)} - 5(3k-6) $ $ {21+3k} - 5(3k-6) $ Distribute the ${-5}$ into the parentheses: $ 21+3k {-5(}\gray{3k-6}{)} $ $ 21+3k {-15k+30} $ Rewrite the expression to group the ${k}$ terms and numeric terms: $ {3k - 15k} + {21 + 30}$ Combine the ${k}$ terms: $ {-12k} + {21 + 30}$ Combine the numeric terms: $ {-12k} + {51}$ The simplified expression is $-12k+51$